Explicit black hole solutions in higher-derivative gravity

TL;DR

This paper derives explicit metrics for all spherically symmetric black holes in Einstein-Weyl theory, revealing how the Bach tensor influences their geometry and thermodynamics, and enabling detailed analysis beyond previous numerical methods.

Contribution

It provides an explicit form of the black hole metric in higher-derivative gravity, including a parameter for the Bach tensor, facilitating analytical study of their properties.

Findings

Explicit Schwarzschild-Bach black hole metrics derived

Bach tensor parameter affects tidal and thermodynamical properties

New form simplifies analysis compared to previous numerical approaches

Abstract

We present, in an explicit form, the metric for all spherically symmetric Schwarzschild-Bach black holes in Einstein-Weyl theory. In addition to the black hole mass, this complete family of spacetimes involves a parameter that encodes the value of the Bach tensor on the horizon. When this additional "non-Schwarzschild parameter" is set to zero the Bach tensor vanishes everywhere and the "Schwa-Bach" solution reduces to the standard Schwarzschild metric of general relativity. Compared with previous studies, which were mainly based on numerical integration of a complicated form of field equations, the new form of the metric enables us to easily investigate geometrical and physical properties of these black holes, such as specific tidal effects on test particles, caused by the presence of the Bach tensor, as well as fundamental thermodynamical quantities.